Cottage Insulation, HELP!


I'm restoring a small barn (10' wide x 16' deep, with a 4' x 8' side lean-to). It's built over a hillside, and supported by steel columns placed in concrete footings, which replaced the old wood pilings. The entire frame is 2" x 4" construction, including the rafters.
Here's the problem: I live in NY State, and need to insulate the barn well in order to use it in Winter, as a home office. The building code calls for R38 in the ceiling, and a minimum of R11 for the exterior walls.
The walls are no problem, since I can install an R15 batt insulation, and although I'd like a higher R value, I can't get it unless I build out the studs to 2' x 6".
The problem is that the 2' x 4' rafters aren't deep enough for adequate insulation. So here are my choices, and I need some advice from someone knowedgable.
Forgot to mention that I'm replacing the roof.
1. Replace the 2" x 4" rafters with at least 2' x 8", or even 2" x 12" rafters, and put the highest R value batt insulation available,
or,
2. Leave the existing rafters, and use 2 layers of rigid foam insulation over the new plywood roof sheating. I saw some R12 rigid foam insulation at Home Depot, so 2 layers of that (R24) and batt insulation (R 15, gives me R39.
What's the best (and least expensive) solution? Thanks!
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snipped-for-privacy@gmail.com wrote:

Do you have a flat or cathedral style ceiling?
If you have a flat ceiling, what about just putting R38 worth of insulation in the ceiling and having it stick up into the attic area?
With a cathedral ceiling you have a bit more hassle, since you don't want to put insulation right up against the bottom of the roof--you generally want airflow there. You can add furring strips to the rafters (to allow for thicker batts), add rigid foam, or use a combination of the two techniques.
In any case you'll want to vapour-barrier the warm side of the insulation, and ensure that the attic has sufficient venting/airflow so that the roof itself stays cold in winter. This will minimize the chances of ice dams.
Chris
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could insulate, if you want R38 in the roof, you will need 12" of fiberglass PLUS a ventilation space. I would guress the cheapest way to attain that would be to build down the existing rafters with another 2x4 which could be hung with plywood gussets. this system would reduce thermal bridging which is a good thing. then install r 38 batts. foam would be a nice way to go but it is expensive in comparison to fiberglass. if you lay foam on top of the roof, you will need to add another layer of plywood on top of that (though if it's steel, i suppose you could just add some firring.).
BTW, i once owned a house that had 2x4 walls. I firred them out with 2x2's and insulated with r 21 batts. was quite easy and worth it i thought.
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